论文标题
贝塞尔过程的零命中时间和焊接同构$_κ$的连续性
Continuity of Zero-Hitting Times of Bessel Processes and Welding Homeomorphisms of SLE$_κ$
论文作者
论文摘要
我们考虑了一个取决于起点$ x $和Dimension $δ$的贝塞尔过程的家族，但是由相同的布朗尼运动驱动的。我们的主要结果是，几乎可以肯定的是，流程首次达到$ 0 $是在$ x $和$δ$中共同连续的，提供了$δ\ le 0 $。作为一个应用程序，我们表明SLE（$κ$）同构同态在[0,4] $中的$κ\中连续$κ$。我们背后的动机是研究$κ$ $_κ$连续性的众所周知的问题。我们证明的主要工具是随机步行，以无限平均逆伽马定律分配的增量。
We consider a family of Bessel Processes that depend on the starting point $x$ and dimension $δ$, but are driven by the same Brownian motion. Our main result is that almost surely the first time a process hits $0$ is jointly continuous in $x$ and $δ$, provided $δ\le 0$. As an application, we show that the SLE($κ$) welding homeomorphism is continuous in $κ$ for $κ\in [0,4]$. Our motivation behind this is to study the well known problem of the continuity of SLE$_κ$ in $κ$. The main tool in our proofs is random walks with increments distributed as infinite mean Inverse-Gamma laws.
